"This has been a very difficult decision for me and my family as I have great respect for the club. I thoroughly enjoyed my time there as manager and would have loved the opportunity to have taken the club on to the next level."
Appointing Hoddle was opposed by key members of Southampton's PLC board. It is understood they feared a backlash from fans could hit the club's share price.
Chairman Lowe appeared to be surprised when he learned of Hoddle's decision today. He said: "He was an option but if he has withdrawn his candidacy then he is no longer an option."
Supporters were furious when Hoddle walked out on the club to join Spurs in March 2001 and then returned to buy star defender Dean Richards.
The former England boss had asked fans to give him a second chance, but a series of anti-Hoddle demonstrations left the club in no doubt about their views.
David Platt has now emerged as a surprise contender to succeed Gordon Strachan.
The England Under-21 coach was at Ewood Park on Saturday to watch Saints' 1-1 draw with Blackburn and is a friend of Wigley, who was his assistant at Nottingham Forest from 1999 to 2001.
However, Platt had an unimpressive record at Forest, winning just 37 of 103 games and making a series of big-money purchases who flopped.
Other contenders for the post include Leeds coach Kevin Blackwell and former Marseille boss Alain Perrin.
